Question

The additive inverse of $\frac{4}{5}\times \frac{2}{3}+\frac{1}{2}\times \frac{4}{5}$ is .

• A. $-\frac{4}{5}$
• B. $-\frac{14}{15}$
• C. $-\frac{8}{13}$

Answer 1

The correct option is B $-\frac{14}{15}$

Given: $\frac{4}{5}\times \frac{2}{3}+\frac{1}{2}\times \frac{4}{5}$

Using commutative property (a + b = b + a)
$\frac{4}{5}\times \frac{2}{3}+\frac{1}{2}\times \frac{4}{5}$ = $\frac{4}{5}\times \frac{2}{3}+\frac{4}{5}\times \frac{1}{2}$

Using distributive property a $\times$ (b + c) = $a\times b+a\times c$

$\frac{4}{5}\times \frac{2}{3}+\frac{1}{2}\times \frac{4}{5}$ = $\frac{4}{5}\times (\frac{2}{3}+\frac{1}{2})$

$\frac{4}{5}\times \frac{2}{3}+\frac{1}{2}\times \frac{4}{5}$ = $\frac{4}{5}\times \left(\frac{4+3}{6}\right)$

$\frac{4}{5}\times \frac{2}{3}+\frac{1}{2}\times \frac{4}{5}$ = $\frac{4}{5}\times \frac{7}{6}$

$\frac{4}{5}\times \frac{2}{3}+\frac{1}{2}\times \frac{4}{5}$ = $\frac{14}{15}$

We know that additive inverse of a is -a.
So, additive inverse of $\frac{14}{15}$ is $-\frac{14}{15}$.